0-恰当半群

0-adequate semigroups

引入了0-恰当半群的概念,它是一种特殊的逆半群.给出了0-恰当半群的等价刻划.讨论具有幂等半格的右0-恰当半群上含于■0的最大同余关系μL和具有幂等半格的0-恰当半群上含于■0的最大同余关系μ.证明如果S是一个具有幂等半格E的右0-A型半群,则S/μL≌E当且仅当S是一个S0左逆的左消含幺半群的强半格.进一步证明了,如果S是一个具有幂等半格E的0-恰当半群,则S/μ≌E当且仅当S是一个S0逆的消去含幺半群的强半格.

We introduce the concept of 0-adequate semigroups. It is a special inverse semigroup. We give the characterizations of 0-adequate semigroups. We discuss the largest congruence μL. contained in L^0 on a right 0-adequate semigroup with semilattice of idempotents E and the largest congruence μ contained in ,H^0 on a 0-adequate semigroup with semilattice of idempotents E. We prove that if S is a right 0-A type semigroup with semilattice of idempotents E, then S/μL≌E if and only if S is a strong semilattice of S^0 left inverse left cancellative monoids. Moreover, we show that if S is a 0-adequate semigroup with semilattice idempotens, then S/μL≌E if and only if S is a strong semilattice of SO inverse cancellative monoids.